;(function (globalObject) {
    'use strict';
  
  /*
   *      bignumber.js v9.0.1
   *      A JavaScript library for arbitrary-precision arithmetic.
   *      https://github.com/MikeMcl/bignumber.js
   *      Copyright (c) 2020 Michael Mclaughlin <M8ch88l@gmail.com>
   *      MIT Licensed.
   *
   *      BigNumber.prototype methods     |  BigNumber methods
   *                                      |
   *      absoluteValue            abs    |  clone
   *      comparedTo                      |  config               set
   *      decimalPlaces            dp     |      DECIMAL_PLACES
   *      dividedBy                div    |      ROUNDING_MODE
   *      dividedToIntegerBy       idiv   |      EXPONENTIAL_AT
   *      exponentiatedBy          pow    |      RANGE
   *      integerValue                    |      CRYPTO
   *      isEqualTo                eq     |      MODULO_MODE
   *      isFinite                        |      POW_PRECISION
   *      isGreaterThan            gt     |      FORMAT
   *      isGreaterThanOrEqualTo   gte    |      ALPHABET
   *      isInteger                       |  isBigNumber
   *      isLessThan               lt     |  maximum              max
   *      isLessThanOrEqualTo      lte    |  minimum              min
   *      isNaN                           |  random
   *      isNegative                      |  sum
   *      isPositive                      |
   *      isZero                          |
   *      minus                           |
   *      modulo                   mod    |
   *      multipliedBy             times  |
   *      negated                         |
   *      plus                            |
   *      precision                sd     |
   *      shiftedBy                       |
   *      squareRoot               sqrt   |
   *      toExponential                   |
   *      toFixed                         |
   *      toFormat                        |
   *      toFraction                      |
   *      toJSON                          |
   *      toNumber                        |
   *      toPrecision                     |
   *      toString                        |
   *      valueOf                         |
   *
   */
  
  
    var BigNumber,
      isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
      mathceil = Math.ceil,
      mathfloor = Math.floor,
  
      bignumberError = '[BigNumber Error] ',
      tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
  
      BASE = 1e14,
      LOG_BASE = 14,
      MAX_SAFE_INTEGER = 0x1fffffffffffff,         // 2^53 - 1
      // MAX_INT32 = 0x7fffffff,                   // 2^31 - 1
      POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
      SQRT_BASE = 1e7,
  
      // EDITABLE
      // The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
      // the arguments to toExponential, toFixed, toFormat, and toPrecision.
      MAX = 1E9;                                   // 0 to MAX_INT32
  
  
    /*
     * Create and return a BigNumber constructor.
     */
    function clone(configObject) {
      var div, convertBase, parseNumeric,
        P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null },
        ONE = new BigNumber(1),
  
  
        //----------------------------- EDITABLE CONFIG DEFAULTS -------------------------------
  
  
        // The default values below must be integers within the inclusive ranges stated.
        // The values can also be changed at run-time using BigNumber.set.
  
        // The maximum number of decimal places for operations involving division.
        DECIMAL_PLACES = 20,                     // 0 to MAX
  
        // The rounding mode used when rounding to the above decimal places, and when using
        // toExponential, toFixed, toFormat and toPrecision, and round (default value).
        // UP         0 Away from zero.
        // DOWN       1 Towards zero.
        // CEIL       2 Towards +Infinity.
        // FLOOR      3 Towards -Infinity.
        // HALF_UP    4 Towards nearest neighbour. If equidistant, up.
        // HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
        // HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
        // HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
        // HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
        ROUNDING_MODE = 4,                       // 0 to 8
  
        // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]
  
        // The exponent value at and beneath which toString returns exponential notation.
        // Number type: -7
        TO_EXP_NEG = -7,                         // 0 to -MAX
  
        // The exponent value at and above which toString returns exponential notation.
        // Number type: 21
        TO_EXP_POS = 21,                         // 0 to MAX
  
        // RANGE : [MIN_EXP, MAX_EXP]
  
        // The minimum exponent value, beneath which underflow to zero occurs.
        // Number type: -324  (5e-324)
        MIN_EXP = -1e7,                          // -1 to -MAX
  
        // The maximum exponent value, above which overflow to Infinity occurs.
        // Number type:  308  (1.7976931348623157e+308)
        // For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
        MAX_EXP = 1e7,                           // 1 to MAX
  
        // Whether to use cryptographically-secure random number generation, if available.
        CRYPTO = false,                          // true or false
  
        // The modulo mode used when calculating the modulus: a mod n.
        // The quotient (q = a / n) is calculated according to the corresponding rounding mode.
        // The remainder (r) is calculated as: r = a - n * q.
        //
        // UP        0 The remainder is positive if the dividend is negative, else is negative.
        // DOWN      1 The remainder has the same sign as the dividend.
        //             This modulo mode is commonly known as 'truncated division' and is
        //             equivalent to (a % n) in JavaScript.
        // FLOOR     3 The remainder has the same sign as the divisor (Python %).
        // HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
        // EUCLID    9 Euclidian division. q = sign(n) * floor(a / abs(n)).
        //             The remainder is always positive.
        //
        // The truncated division, floored division, Euclidian division and IEEE 754 remainder
        // modes are commonly used for the modulus operation.
        // Although the other rounding modes can also be used, they may not give useful results.
        MODULO_MODE = 1,                         // 0 to 9
  
        // The maximum number of significant digits of the result of the exponentiatedBy operation.
        // If POW_PRECISION is 0, there will be unlimited significant digits.
        POW_PRECISION = 0,                    // 0 to MAX
  
        // The format specification used by the BigNumber.prototype.toFormat method.
        FORMAT = {
          prefix: '',
          groupSize: 3,
          secondaryGroupSize: 0,
          groupSeparator: ',',
          decimalSeparator: '.',
          fractionGroupSize: 0,
          fractionGroupSeparator: '\xA0',      // non-breaking space
          suffix: ''
        },
  
        // The alphabet used for base conversion. It must be at least 2 characters long, with no '+',
        // '-', '.', whitespace, or repeated character.
        // '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
        ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
  
  
      //------------------------------------------------------------------------------------------
  
  
      // CONSTRUCTOR
  
  
      /*
       * The BigNumber constructor and exported function.
       * Create and return a new instance of a BigNumber object.
       *
       * v {number|string|BigNumber} A numeric value.
       * [b] {number} The base of v. Integer, 2 to ALPHABET.length inclusive.
       */
      function BigNumber(v, b) {
        var alphabet, c, caseChanged, e, i, isNum, len, str,
          x = this;
  
        // Enable constructor call without `new`.
        if (!(x instanceof BigNumber)) return new BigNumber(v, b);
  
        if (b == null) {
  
          if (v && v._isBigNumber === true) {
            x.s = v.s;
  
            if (!v.c || v.e > MAX_EXP) {
              x.c = x.e = null;
            } else if (v.e < MIN_EXP) {
              x.c = [x.e = 0];
            } else {
              x.e = v.e;
              x.c = v.c.slice();
            }
  
            return;
          }
  
          if ((isNum = typeof v == 'number') && v * 0 == 0) {
  
            // Use `1 / n` to handle minus zero also.
            x.s = 1 / v < 0 ? (v = -v, -1) : 1;
  
            // Fast path for integers, where n < 2147483648 (2**31).
            if (v === ~~v) {
              for (e = 0, i = v; i >= 10; i /= 10, e++);
  
              if (e > MAX_EXP) {
                x.c = x.e = null;
              } else {
                x.e = e;
                x.c = [v];
              }
  
              return;
            }
  
            str = String(v);
          } else {
  
            if (!isNumeric.test(str = String(v))) return parseNumeric(x, str, isNum);
  
            x.s = str.charCodeAt(0) == 45 ? (str = str.slice(1), -1) : 1;
          }
  
          // Decimal point?
          if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
  
          // Exponential form?
          if ((i = str.search(/e/i)) > 0) {
  
            // Determine exponent.
            if (e < 0) e = i;
            e += +str.slice(i + 1);
            str = str.substring(0, i);
          } else if (e < 0) {
  
            // Integer.
            e = str.length;
          }
  
        } else {
  
          // '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
          intCheck(b, 2, ALPHABET.length, 'Base');
  
          // Allow exponential notation to be used with base 10 argument, while
          // also rounding to DECIMAL_PLACES as with other bases.
          if (b == 10) {
            x = new BigNumber(v);
            return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
          }
  
          str = String(v);
  
          if (isNum = typeof v == 'number') {
  
            // Avoid potential interpretation of Infinity and NaN as base 44+ values.
            if (v * 0 != 0) return parseNumeric(x, str, isNum, b);
  
            x.s = 1 / v < 0 ? (str = str.slice(1), -1) : 1;
  
            // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
            if (BigNumber.DEBUG && str.replace(/^0\.0*|\./, '').length > 15) {
              throw Error
               (tooManyDigits + v);
            }
          } else {
            x.s = str.charCodeAt(0) === 45 ? (str = str.slice(1), -1) : 1;
          }
  
          alphabet = ALPHABET.slice(0, b);
          e = i = 0;
  
          // Check that str is a valid base b number.
          // Don't use RegExp, so alphabet can contain special characters.
          for (len = str.length; i < len; i++) {
            if (alphabet.indexOf(c = str.charAt(i)) < 0) {
              if (c == '.') {
  
                // If '.' is not the first character and it has not be found before.
                if (i > e) {
                  e = len;
                  continue;
                }
              } else if (!caseChanged) {
  
                // Allow e.g. hexadecimal 'FF' as well as 'ff'.
                if (str == str.toUpperCase() && (str = str.toLowerCase()) ||
                    str == str.toLowerCase() && (str = str.toUpperCase())) {
                  caseChanged = true;
                  i = -1;
                  e = 0;
                  continue;
                }
              }
  
              return parseNumeric(x, String(v), isNum, b);
            }
          }
  
          // Prevent later check for length on converted number.
          isNum = false;
          str = convertBase(str, b, 10, x.s);
  
          // Decimal point?
          if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
          else e = str.length;
        }
  
        // Determine leading zeros.
        for (i = 0; str.charCodeAt(i) === 48; i++);
  
        // Determine trailing zeros.
        for (len = str.length; str.charCodeAt(--len) === 48;);
  
        if (str = str.slice(i, ++len)) {
          len -= i;
  
          // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
          if (isNum && BigNumber.DEBUG &&
            len > 15 && (v > MAX_SAFE_INTEGER || v !== mathfloor(v))) {
              throw Error
               (tooManyDigits + (x.s * v));
          }
  
           // Overflow?
          if ((e = e - i - 1) > MAX_EXP) {
  
            // Infinity.
            x.c = x.e = null;
  
          // Underflow?
          } else if (e < MIN_EXP) {
  
            // Zero.
            x.c = [x.e = 0];
          } else {
            x.e = e;
            x.c = [];
  
            // Transform base
  
            // e is the base 10 exponent.
            // i is where to slice str to get the first element of the coefficient array.
            i = (e + 1) % LOG_BASE;
            if (e < 0) i += LOG_BASE;  // i < 1
  
            if (i < len) {
              if (i) x.c.push(+str.slice(0, i));
  
              for (len -= LOG_BASE; i < len;) {
                x.c.push(+str.slice(i, i += LOG_BASE));
              }
  
              i = LOG_BASE - (str = str.slice(i)).length;
            } else {
              i -= len;
            }
  
            for (; i--; str += '0');
            x.c.push(+str);
          }
        } else {
  
          // Zero.
          x.c = [x.e = 0];
        }
      }
  
  
      // CONSTRUCTOR PROPERTIES
  
  
      BigNumber.clone = clone;
  
      BigNumber.ROUND_UP = 0;
      BigNumber.ROUND_DOWN = 1;
      BigNumber.ROUND_CEIL = 2;
      BigNumber.ROUND_FLOOR = 3;
      BigNumber.ROUND_HALF_UP = 4;
      BigNumber.ROUND_HALF_DOWN = 5;
      BigNumber.ROUND_HALF_EVEN = 6;
      BigNumber.ROUND_HALF_CEIL = 7;
      BigNumber.ROUND_HALF_FLOOR = 8;
      BigNumber.EUCLID = 9;
  
  
      /*
       * Configure infrequently-changing library-wide settings.
       *
       * Accept an object with the following optional properties (if the value of a property is
       * a number, it must be an integer within the inclusive range stated):
       *
       *   DECIMAL_PLACES   {number}           0 to MAX
       *   ROUNDING_MODE    {number}           0 to 8
       *   EXPONENTIAL_AT   {number|number[]}  -MAX to MAX  or  [-MAX to 0, 0 to MAX]
       *   RANGE            {number|number[]}  -MAX to MAX (not zero)  or  [-MAX to -1, 1 to MAX]
       *   CRYPTO           {boolean}          true or false
       *   MODULO_MODE      {number}           0 to 9
       *   POW_PRECISION       {number}           0 to MAX
       *   ALPHABET         {string}           A string of two or more unique characters which does
       *                                       not contain '.'.
       *   FORMAT           {object}           An object with some of the following properties:
       *     prefix                 {string}
       *     groupSize              {number}
       *     secondaryGroupSize     {number}
       *     groupSeparator         {string}
       *     decimalSeparator       {string}
       *     fractionGroupSize      {number}
       *     fractionGroupSeparator {string}
       *     suffix                 {string}
       *
       * (The values assigned to the above FORMAT object properties are not checked for validity.)
       *
       * E.g.
       * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
       *
       * Ignore properties/parameters set to null or undefined, except for ALPHABET.
       *
       * Return an object with the properties current values.
       */
      BigNumber.config = BigNumber.set = function (obj) {
        var p, v;
  
        if (obj != null) {
  
          if (typeof obj == 'object') {
  
            // DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
            // '[BigNumber Error] DECIMAL_PLACES {not a primitive number|not an integer|out of range}: {v}'
            if (obj.hasOwnProperty(p = 'DECIMAL_PLACES')) {
              v = obj[p];
              intCheck(v, 0, MAX, p);
              DECIMAL_PLACES = v;
            }
  
            // ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
            // '[BigNumber Error] ROUNDING_MODE {not a primitive number|not an integer|out of range}: {v}'
            if (obj.hasOwnProperty(p = 'ROUNDING_MODE')) {
              v = obj[p];
              intCheck(v, 0, 8, p);
              ROUNDING_MODE = v;
            }
  
            // EXPONENTIAL_AT {number|number[]}
            // Integer, -MAX to MAX inclusive or
            // [integer -MAX to 0 inclusive, 0 to MAX inclusive].
            // '[BigNumber Error] EXPONENTIAL_AT {not a primitive number|not an integer|out of range}: {v}'
            if (obj.hasOwnProperty(p = 'EXPONENTIAL_AT')) {
              v = obj[p];
              if (v && v.pop) {
                intCheck(v[0], -MAX, 0, p);
                intCheck(v[1], 0, MAX, p);
                TO_EXP_NEG = v[0];
                TO_EXP_POS = v[1];
              } else {
                intCheck(v, -MAX, MAX, p);
                TO_EXP_NEG = -(TO_EXP_POS = v < 0 ? -v : v);
              }
            }
  
            // RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
            // [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
            // '[BigNumber Error] RANGE {not a primitive number|not an integer|out of range|cannot be zero}: {v}'
            if (obj.hasOwnProperty(p = 'RANGE')) {
              v = obj[p];
              if (v && v.pop) {
                intCheck(v[0], -MAX, -1, p);
                intCheck(v[1], 1, MAX, p);
                MIN_EXP = v[0];
                MAX_EXP = v[1];
              } else {
                intCheck(v, -MAX, MAX, p);
                if (v) {
                  MIN_EXP = -(MAX_EXP = v < 0 ? -v : v);
                } else {
                  throw Error
                   (bignumberError + p + ' cannot be zero: ' + v);
                }
              }
            }
  
            // CRYPTO {boolean} true or false.
            // '[BigNumber Error] CRYPTO not true or false: {v}'
            // '[BigNumber Error] crypto unavailable'
            if (obj.hasOwnProperty(p = 'CRYPTO')) {
              v = obj[p];
              if (v === !!v) {
                if (v) {
                  if (typeof crypto != 'undefined' && crypto &&
                   (crypto.getRandomValues || crypto.randomBytes)) {
                    CRYPTO = v;
                  } else {
                    CRYPTO = !v;
                    throw Error
                     (bignumberError + 'crypto unavailable');
                  }
                } else {
                  CRYPTO = v;
                }
              } else {
                throw Error
                 (bignumberError + p + ' not true or false: ' + v);
              }
            }
  
            // MODULO_MODE {number} Integer, 0 to 9 inclusive.
            // '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
            if (obj.hasOwnProperty(p = 'MODULO_MODE')) {
              v = obj[p];
              intCheck(v, 0, 9, p);
              MODULO_MODE = v;
            }
  
            // POW_PRECISION {number} Integer, 0 to MAX inclusive.
            // '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
            if (obj.hasOwnProperty(p = 'POW_PRECISION')) {
              v = obj[p];
              intCheck(v, 0, MAX, p);
              POW_PRECISION = v;
            }
  
            // FORMAT {object}
            // '[BigNumber Error] FORMAT not an object: {v}'
            if (obj.hasOwnProperty(p = 'FORMAT')) {
              v = obj[p];
              if (typeof v == 'object') FORMAT = v;
              else throw Error
               (bignumberError + p + ' not an object: ' + v);
            }
  
            // ALPHABET {string}
            // '[BigNumber Error] ALPHABET invalid: {v}'
            if (obj.hasOwnProperty(p = 'ALPHABET')) {
              v = obj[p];
  
              // Disallow if less than two characters,
              // or if it contains '+', '-', '.', whitespace, or a repeated character.
              if (typeof v == 'string' && !/^.?$|[+\-.\s]|(.).*\1/.test(v)) {
                ALPHABET = v;
              } else {
                throw Error
                 (bignumberError + p + ' invalid: ' + v);
              }
            }
  
          } else {
  
            // '[BigNumber Error] Object expected: {v}'
            throw Error
             (bignumberError + 'Object expected: ' + obj);
          }
        }
  
        return {
          DECIMAL_PLACES: DECIMAL_PLACES,
          ROUNDING_MODE: ROUNDING_MODE,
          EXPONENTIAL_AT: [TO_EXP_NEG, TO_EXP_POS],
          RANGE: [MIN_EXP, MAX_EXP],
          CRYPTO: CRYPTO,
          MODULO_MODE: MODULO_MODE,
          POW_PRECISION: POW_PRECISION,
          FORMAT: FORMAT,
          ALPHABET: ALPHABET
        };
      };
  
  
      /*
       * Return true if v is a BigNumber instance, otherwise return false.
       *
       * If BigNumber.DEBUG is true, throw if a BigNumber instance is not well-formed.
       *
       * v {any}
       *
       * '[BigNumber Error] Invalid BigNumber: {v}'
       */
      BigNumber.isBigNumber = function (v) {
        if (!v || v._isBigNumber !== true) return false;
        if (!BigNumber.DEBUG) return true;
  
        var i, n,
          c = v.c,
          e = v.e,
          s = v.s;
  
        out: if ({}.toString.call(c) == '[object Array]') {
  
          if ((s === 1 || s === -1) && e >= -MAX && e <= MAX && e === mathfloor(e)) {
  
            // If the first element is zero, the BigNumber value must be zero.
            if (c[0] === 0) {
              if (e === 0 && c.length === 1) return true;
              break out;
            }
  
            // Calculate number of digits that c[0] should have, based on the exponent.
            i = (e + 1) % LOG_BASE;
            if (i < 1) i += LOG_BASE;
  
            // Calculate number of digits of c[0].
            //if (Math.ceil(Math.log(c[0] + 1) / Math.LN10) == i) {
            if (String(c[0]).length == i) {
  
              for (i = 0; i < c.length; i++) {
                n = c[i];
                if (n < 0 || n >= BASE || n !== mathfloor(n)) break out;
              }
  
              // Last element cannot be zero, unless it is the only element.
              if (n !== 0) return true;
            }
          }
  
        // Infinity/NaN
        } else if (c === null && e === null && (s === null || s === 1 || s === -1)) {
          return true;
        }
  
        throw Error
          (bignumberError + 'Invalid BigNumber: ' + v);
      };
  
  
      /*
       * Return a new BigNumber whose value is the maximum of the arguments.
       *
       * arguments {number|string|BigNumber}
       */
      BigNumber.maximum = BigNumber.max = function () {
        return maxOrMin(arguments, P.lt);
      };
  
  
      /*
       * Return a new BigNumber whose value is the minimum of the arguments.
       *
       * arguments {number|string|BigNumber}
       */
      BigNumber.minimum = BigNumber.min = function () {
        return maxOrMin(arguments, P.gt);
      };
  
  
      /*
       * Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
       * and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
       * zeros are produced).
       *
       * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
       *
       * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp}'
       * '[BigNumber Error] crypto unavailable'
       */
      BigNumber.random = (function () {
        var pow2_53 = 0x20000000000000;
  
        // Return a 53 bit integer n, where 0 <= n < 9007199254740992.
        // Check if Math.random() produces more than 32 bits of randomness.
        // If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
        // 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
        var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
         ? function () { return mathfloor(Math.random() * pow2_53); }
         : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
           (Math.random() * 0x800000 | 0); };
  
        return function (dp) {
          var a, b, e, k, v,
            i = 0,
            c = [],
            rand = new BigNumber(ONE);
  
          if (dp == null) dp = DECIMAL_PLACES;
          else intCheck(dp, 0, MAX);
  
          k = mathceil(dp / LOG_BASE);
  
          if (CRYPTO) {
  
            // Browsers supporting crypto.getRandomValues.
            if (crypto.getRandomValues) {
  
              a = crypto.getRandomValues(new Uint32Array(k *= 2));
  
              for (; i < k;) {
  
                // 53 bits:
                // ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
                // 11111 11111111 11111111 11111111 11100000 00000000 00000000
                // ((Math.pow(2, 32) - 1) >>> 11).toString(2)
                //                                     11111 11111111 11111111
                // 0x20000 is 2^21.
                v = a[i] * 0x20000 + (a[i + 1] >>> 11);
  
                // Rejection sampling:
                // 0 <= v < 9007199254740992
                // Probability that v >= 9e15, is
                // 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
                if (v >= 9e15) {
                  b = crypto.getRandomValues(new Uint32Array(2));
                  a[i] = b[0];
                  a[i + 1] = b[1];
                } else {
  
                  // 0 <= v <= 8999999999999999
                  // 0 <= (v % 1e14) <= 99999999999999
                  c.push(v % 1e14);
                  i += 2;
                }
              }
              i = k / 2;
  
            // Node.js supporting crypto.randomBytes.
            } else if (crypto.randomBytes) {
  
              // buffer
              a = crypto.randomBytes(k *= 7);
  
              for (; i < k;) {
  
                // 0x1000000000000 is 2^48, 0x10000000000 is 2^40
                // 0x100000000 is 2^32, 0x1000000 is 2^24
                // 11111 11111111 11111111 11111111 11111111 11111111 11111111
                // 0 <= v < 9007199254740992
                v = ((a[i] & 31) * 0x1000000000000) + (a[i + 1] * 0x10000000000) +
                   (a[i + 2] * 0x100000000) + (a[i + 3] * 0x1000000) +
                   (a[i + 4] << 16) + (a[i + 5] << 8) + a[i + 6];
  
                if (v >= 9e15) {
                  crypto.randomBytes(7).copy(a, i);
                } else {
  
                  // 0 <= (v % 1e14) <= 99999999999999
                  c.push(v % 1e14);
                  i += 7;
                }
              }
              i = k / 7;
            } else {
              CRYPTO = false;
              throw Error
               (bignumberError + 'crypto unavailable');
            }
          }
  
          // Use Math.random.
          if (!CRYPTO) {
  
            for (; i < k;) {
              v = random53bitInt();
              if (v < 9e15) c[i++] = v % 1e14;
            }
          }
  
          k = c[--i];
          dp %= LOG_BASE;
  
          // Convert trailing digits to zeros according to dp.
          if (k && dp) {
            v = POWS_TEN[LOG_BASE - dp];
            c[i] = mathfloor(k / v) * v;
          }
  
          // Remove trailing elements which are zero.
          for (; c[i] === 0; c.pop(), i--);
  
          // Zero?
          if (i < 0) {
            c = [e = 0];
          } else {
  
            // Remove leading elements which are zero and adjust exponent accordingly.
            for (e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
  
            // Count the digits of the first element of c to determine leading zeros, and...
            for (i = 1, v = c[0]; v >= 10; v /= 10, i++);
  
            // adjust the exponent accordingly.
            if (i < LOG_BASE) e -= LOG_BASE - i;
          }
  
          rand.e = e;
          rand.c = c;
          return rand;
        };
      })();
  
  
      /*
       * Return a BigNumber whose value is the sum of the arguments.
       *
       * arguments {number|string|BigNumber}
       */
      BigNumber.sum = function () {
        var i = 1,
          args = arguments,
          sum = new BigNumber(args[0]);
        for (; i < args.length;) sum = sum.plus(args[i++]);
        return sum;
      };
  
  
      // PRIVATE FUNCTIONS
  
  
      // Called by BigNumber and BigNumber.prototype.toString.
      convertBase = (function () {
        var decimal = '0123456789';
  
        /*
         * Convert string of baseIn to an array of numbers of baseOut.
         * Eg. toBaseOut('255', 10, 16) returns [15, 15].
         * Eg. toBaseOut('ff', 16, 10) returns [2, 5, 5].
         */
        function toBaseOut(str, baseIn, baseOut, alphabet) {
          var j,
            arr = [0],
            arrL,
            i = 0,
            len = str.length;
  
          for (; i < len;) {
            for (arrL = arr.length; arrL--; arr[arrL] *= baseIn);
  
            arr[0] += alphabet.indexOf(str.charAt(i++));
  
            for (j = 0; j < arr.length; j++) {
  
              if (arr[j] > baseOut - 1) {
                if (arr[j + 1] == null) arr[j + 1] = 0;
                arr[j + 1] += arr[j] / baseOut | 0;
                arr[j] %= baseOut;
              }
            }
          }
  
          return arr.reverse();
        }
  
        // Convert a numeric string of baseIn to a numeric string of baseOut.
        // If the caller is toString, we are converting from base 10 to baseOut.
        // If the caller is BigNumber, we are converting from baseIn to base 10.
        return function (str, baseIn, baseOut, sign, callerIsToString) {
          var alphabet, d, e, k, r, x, xc, y,
            i = str.indexOf('.'),
            dp = DECIMAL_PLACES,
            rm = ROUNDING_MODE;
  
          // Non-integer.
          if (i >= 0) {
            k = POW_PRECISION;
  
            // Unlimited precision.
            POW_PRECISION = 0;
            str = str.replace('.', '');
            y = new BigNumber(baseIn);
            x = y.pow(str.length - i);
            POW_PRECISION = k;
  
            // Convert str as if an integer, then restore the fraction part by dividing the
            // result by its base raised to a power.
  
            y.c = toBaseOut(toFixedPoint(coeffToString(x.c), x.e, '0'),
             10, baseOut, decimal);
            y.e = y.c.length;
          }
  
          // Convert the number as integer.
  
          xc = toBaseOut(str, baseIn, baseOut, callerIsToString
           ? (alphabet = ALPHABET, decimal)
           : (alphabet = decimal, ALPHABET));
  
          // xc now represents str as an integer and converted to baseOut. e is the exponent.
          e = k = xc.length;
  
          // Remove trailing zeros.
          for (; xc[--k] == 0; xc.pop());
  
          // Zero?
          if (!xc[0]) return alphabet.charAt(0);
  
          // Does str represent an integer? If so, no need for the division.
          if (i < 0) {
            --e;
          } else {
            x.c = xc;
            x.e = e;
  
            // The sign is needed for correct rounding.
            x.s = sign;
            x = div(x, y, dp, rm, baseOut);
            xc = x.c;
            r = x.r;
            e = x.e;
          }
  
          // xc now represents str converted to baseOut.
  
          // THe index of the rounding digit.
          d = e + dp + 1;
  
          // The rounding digit: the digit to the right of the digit that may be rounded up.
          i = xc[d];
  
          // Look at the rounding digits and mode to determine whether to round up.
  
          k = baseOut / 2;
          r = r || d < 0 || xc[d + 1] != null;
  
          r = rm < 4 ? (i != null || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
                : i > k || i == k &&(rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
                 rm == (x.s < 0 ? 8 : 7));
  
          // If the index of the rounding digit is not greater than zero, or xc represents
          // zero, then the result of the base conversion is zero or, if rounding up, a value
          // such as 0.00001.
          if (d < 1 || !xc[0]) {
  
            // 1^-dp or 0
            str = r ? toFixedPoint(alphabet.charAt(1), -dp, alphabet.charAt(0)) : alphabet.charAt(0);
          } else {
  
            // Truncate xc to the required number of decimal places.
            xc.length = d;
  
            // Round up?
            if (r) {
  
              // Rounding up may mean the previous digit has to be rounded up and so on.
              for (--baseOut; ++xc[--d] > baseOut;) {
                xc[d] = 0;
  
                if (!d) {
                  ++e;
                  xc = [1].concat(xc);
                }
              }
            }
  
            // Determine trailing zeros.
            for (k = xc.length; !xc[--k];);
  
            // E.g. [4, 11, 15] becomes 4bf.
            for (i = 0, str = ''; i <= k; str += alphabet.charAt(xc[i++]));
  
            // Add leading zeros, decimal point and trailing zeros as required.
            str = toFixedPoint(str, e, alphabet.charAt(0));
          }
  
          // The caller will add the sign.
          return str;
        };
      })();
  
  
      // Perform division in the specified base. Called by div and convertBase.
      div = (function () {
  
        // Assume non-zero x and k.
        function multiply(x, k, base) {
          var m, temp, xlo, xhi,
            carry = 0,
            i = x.length,
            klo = k % SQRT_BASE,
            khi = k / SQRT_BASE | 0;
  
          for (x = x.slice(); i--;) {
            xlo = x[i] % SQRT_BASE;
            xhi = x[i] / SQRT_BASE | 0;
            m = khi * xlo + xhi * klo;
            temp = klo * xlo + ((m % SQRT_BASE) * SQRT_BASE) + carry;
            carry = (temp / base | 0) + (m / SQRT_BASE | 0) + khi * xhi;
            x[i] = temp % base;
          }
  
          if (carry) x = [carry].concat(x);
  
          return x;
        }
  
        function compare(a, b, aL, bL) {
          var i, cmp;
  
          if (aL != bL) {
            cmp = aL > bL ? 1 : -1;
          } else {
  
            for (i = cmp = 0; i < aL; i++) {
  
              if (a[i] != b[i]) {
                cmp = a[i] > b[i] ? 1 : -1;
                break;
              }
            }
          }
  
          return cmp;
        }
  
        function subtract(a, b, aL, base) {
          var i = 0;
  
          // Subtract b from a.
          for (; aL--;) {
            a[aL] -= i;
            i = a[aL] < b[aL] ? 1 : 0;
            a[aL] = i * base + a[aL] - b[aL];
          }
  
          // Remove leading zeros.
          for (; !a[0] && a.length > 1; a.splice(0, 1));
        }
  
        // x: dividend, y: divisor.
        return function (x, y, dp, rm, base) {
          var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
            yL, yz,
            s = x.s == y.s ? 1 : -1,
            xc = x.c,
            yc = y.c;
  
          // Either NaN, Infinity or 0?
          if (!xc || !xc[0] || !yc || !yc[0]) {
  
            return new BigNumber(
  
             // Return NaN if either NaN, or both Infinity or 0.
             !x.s || !y.s || (xc ? yc && xc[0] == yc[0] : !yc) ? NaN :
  
              // Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
              xc && xc[0] == 0 || !yc ? s * 0 : s / 0
           );
          }
  
          q = new BigNumber(s);
          qc = q.c = [];
          e = x.e - y.e;
          s = dp + e + 1;
  
          if (!base) {
            base = BASE;
            e = bitFloor(x.e / LOG_BASE) - bitFloor(y.e / LOG_BASE);
            s = s / LOG_BASE | 0;
          }
  
          // Result exponent may be one less then the current value of e.
          // The coefficients of the BigNumbers from convertBase may have trailing zeros.
          for (i = 0; yc[i] == (xc[i] || 0); i++);
  
          if (yc[i] > (xc[i] || 0)) e--;
  
          if (s < 0) {
            qc.push(1);
            more = true;
          } else {
            xL = xc.length;
            yL = yc.length;
            i = 0;
            s += 2;
  
            // Normalise xc and yc so highest order digit of yc is >= base / 2.
  
            n = mathfloor(base / (yc[0] + 1));
  
            // Not necessary, but to handle odd bases where yc[0] == (base / 2) - 1.
            // if (n > 1 || n++ == 1 && yc[0] < base / 2) {
            if (n > 1) {
              yc = multiply(yc, n, base);
              xc = multiply(xc, n, base);
              yL = yc.length;
              xL = xc.length;
            }
  
            xi = yL;
            rem = xc.slice(0, yL);
            remL = rem.length;
  
            // Add zeros to make remainder as long as divisor.
            for (; remL < yL; rem[remL++] = 0);
            yz = yc.slice();
            yz = [0].concat(yz);
            yc0 = yc[0];
            if (yc[1] >= base / 2) yc0++;
            // Not necessary, but to prevent trial digit n > base, when using base 3.
            // else if (base == 3 && yc0 == 1) yc0 = 1 + 1e-15;
  
            do {
              n = 0;
  
              // Compare divisor and remainder.
              cmp = compare(yc, rem, yL, remL);
  
              // If divisor < remainder.
              if (cmp < 0) {
  
                // Calculate trial digit, n.
  
                rem0 = rem[0];
                if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
  
                // n is how many times the divisor goes into the current remainder.
                n = mathfloor(rem0 / yc0);
  
                //  Algorithm:
                //  product = divisor multiplied by trial digit (n).
                //  Compare product and remainder.
                //  If product is greater than remainder:
                //    Subtract divisor from product, decrement trial digit.
                //  Subtract product from remainder.
                //  If product was less than remainder at the last compare:
                //    Compare new remainder and divisor.
                //    If remainder is greater than divisor:
                //      Subtract divisor from remainder, increment trial digit.
  
                if (n > 1) {
  
                  // n may be > base only when base is 3.
                  if (n >= base) n = base - 1;
  
                  // product = divisor * trial digit.
                  prod = multiply(yc, n, base);
                  prodL = prod.length;
                  remL = rem.length;
  
                  // Compare product and remainder.
                  // If product > remainder then trial digit n too high.
                  // n is 1 too high about 5% of the time, and is not known to have
                  // ever been more than 1 too high.
                  while (compare(prod, rem, prodL, remL) == 1) {
                    n--;
  
                    // Subtract divisor from product.
                    subtract(prod, yL < prodL ? yz : yc, prodL, base);
                    prodL = prod.length;
                    cmp = 1;
                  }
                } else {
  
                  // n is 0 or 1, cmp is -1.
                  // If n is 0, there is no need to compare yc and rem again below,
                  // so change cmp to 1 to avoid it.
                  // If n is 1, leave cmp as -1, so yc and rem are compared again.
                  if (n == 0) {
  
                    // divisor < remainder, so n must be at least 1.
                    cmp = n = 1;
                  }
  
                  // product = divisor
                  prod = yc.slice();
                  prodL = prod.length;
                }
  
                if (prodL < remL) prod = [0].concat(prod);
  
                // Subtract product from remainder.
                subtract(rem, prod, remL, base);
                remL = rem.length;
  
                 // If product was < remainder.
                if (cmp == -1) {
  
                  // Compare divisor and new remainder.
                  // If divisor < new remainder, subtract divisor from remainder.
                  // Trial digit n too low.
                  // n is 1 too low about 5% of the time, and very rarely 2 too low.
                  while (compare(yc, rem, yL, remL) < 1) {
                    n++;
  
                    // Subtract divisor from remainder.
                    subtract(rem, yL < remL ? yz : yc, remL, base);
                    remL = rem.length;
                  }
                }
              } else if (cmp === 0) {
                n++;
                rem = [0];
              } // else cmp === 1 and n will be 0
  
              // Add the next digit, n, to the result array.
              qc[i++] = n;
  
              // Update the remainder.
              if (rem[0]) {
                rem[remL++] = xc[xi] || 0;
              } else {
                rem = [xc[xi]];
                remL = 1;
              }
            } while ((xi++ < xL || rem[0] != null) && s--);
  
            more = rem[0] != null;
  
            // Leading zero?
            if (!qc[0]) qc.splice(0, 1);
          }
  
          if (base == BASE) {
  
            // To calculate q.e, first get the number of digits of qc[0].
            for (i = 1, s = qc[0]; s >= 10; s /= 10, i++);
  
            round(q, dp + (q.e = i + e * LOG_BASE - 1) + 1, rm, more);
  
          // Caller is convertBase.
          } else {
            q.e = e;
            q.r = +more;
          }
  
          return q;
        };
      })();
  
  
      /*
       * Return a string representing the value of BigNumber n in fixed-point or exponential
       * notation rounded to the specified decimal places or significant digits.
       *
       * n: a BigNumber.
       * i: the index of the last digit required (i.e. the digit that may be rounded up).
       * rm: the rounding mode.
       * id: 1 (toExponential) or 2 (toPrecision).
       */
      function format(n, i, rm, id) {
        var c0, e, ne, len, str;
  
        if (rm == null) rm = ROUNDING_MODE;
        else intCheck(rm, 0, 8);
  
        if (!n.c) return n.toString();
  
        c0 = n.c[0];
        ne = n.e;
  
        if (i == null) {
          str = coeffToString(n.c);
          str = id == 1 || id == 2 && (ne <= TO_EXP_NEG || ne >= TO_EXP_POS)
           ? toExponential(str, ne)
           : toFixedPoint(str, ne, '0');
        } else {
          n = round(new BigNumber(n), i, rm);
  
          // n.e may have changed if the value was rounded up.
          e = n.e;
  
          str = coeffToString(n.c);
          len = str.length;
  
          // toPrecision returns exponential notation if the number of significant digits
          // specified is less than the number of digits necessary to represent the integer
          // part of the value in fixed-point notation.
  
          // Exponential notation.
          if (id == 1 || id == 2 && (i <= e || e <= TO_EXP_NEG)) {
  
            // Append zeros?
            for (; len < i; str += '0', len++);
            str = toExponential(str, e);
  
          // Fixed-point notation.
          } else {
            i -= ne;
            str = toFixedPoint(str, e, '0');
  
            // Append zeros?
            if (e + 1 > len) {
              if (--i > 0) for (str += '.'; i--; str += '0');
            } else {
              i += e - len;
              if (i > 0) {
                if (e + 1 == len) str += '.';
                for (; i--; str += '0');
              }
            }
          }
        }
  
        return n.s < 0 && c0 ? '-' + str : str;
      }
  
  
      // Handle BigNumber.max and BigNumber.min.
      function maxOrMin(args, method) {
        var n,
          i = 1,
          m = new BigNumber(args[0]);
  
        for (; i < args.length; i++) {
          n = new BigNumber(args[i]);
  
          // If any number is NaN, return NaN.
          if (!n.s) {
            m = n;
            break;
          } else if (method.call(m, n)) {
            m = n;
          }
        }
  
        return m;
      }
  
  
      /*
       * Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
       * Called by minus, plus and times.
       */
      function normalise(n, c, e) {
        var i = 1,
          j = c.length;
  
         // Remove trailing zeros.
        for (; !c[--j]; c.pop());
  
        // Calculate the base 10 exponent. First get the number of digits of c[0].
        for (j = c[0]; j >= 10; j /= 10, i++);
  
        // Overflow?
        if ((e = i + e * LOG_BASE - 1) > MAX_EXP) {
  
          // Infinity.
          n.c = n.e = null;
  
        // Underflow?
        } else if (e < MIN_EXP) {
  
          // Zero.
          n.c = [n.e = 0];
        } else {
          n.e = e;
          n.c = c;
        }
  
        return n;
      }
  
  
      // Handle values that fail the validity test in BigNumber.
      parseNumeric = (function () {
        var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
          dotAfter = /^([^.]+)\.$/,
          dotBefore = /^\.([^.]+)$/,
          isInfinityOrNaN = /^-?(Infinity|NaN)$/,
          whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
  
        return function (x, str, isNum, b) {
          var base,
            s = isNum ? str : str.replace(whitespaceOrPlus, '');
  
          // No exception on ±Infinity or NaN.
          if (isInfinityOrNaN.test(s)) {
            x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
          } else {
            if (!isNum) {
  
              // basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
              s = s.replace(basePrefix, function (m, p1, p2) {
                base = (p2 = p2.toLowerCase()) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
                return !b || b == base ? p1 : m;
              });
  
              if (b) {
                base = b;
  
                // E.g. '1.' to '1', '.1' to '0.1'
                s = s.replace(dotAfter, '$1').replace(dotBefore, '0.$1');
              }
  
              if (str != s) return new BigNumber(s, base);
            }
  
            // '[BigNumber Error] Not a number: {n}'
            // '[BigNumber Error] Not a base {b} number: {n}'
            if (BigNumber.DEBUG) {
              throw Error
                (bignumberError + 'Not a' + (b ? ' base ' + b : '') + ' number: ' + str);
            }
  
            // NaN
            x.s = null;
          }
  
          x.c = x.e = null;
        }
      })();
  
  
      /*
       * Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
       * If r is truthy, it is known that there are more digits after the rounding digit.
       */
      function round(x, sd, rm, r) {
        var d, i, j, k, n, ni, rd,
          xc = x.c,
          pows10 = POWS_TEN;
  
        // if x is not Infinity or NaN...
        if (xc) {
  
          // rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
          // n is a base 1e14 number, the value of the element of array x.c containing rd.
          // ni is the index of n within x.c.
          // d is the number of digits of n.
          // i is the index of rd within n including leading zeros.
          // j is the actual index of rd within n (if < 0, rd is a leading zero).
          out: {
  
            // Get the number of digits of the first element of xc.
            for (d = 1, k = xc[0]; k >= 10; k /= 10, d++);
            i = sd - d;
  
            // If the rounding digit is in the first element of xc...
            if (i < 0) {
              i += LOG_BASE;
              j = sd;
              n = xc[ni = 0];
  
              // Get the rounding digit at index j of n.
              rd = n / pows10[d - j - 1] % 10 | 0;
            } else {
              ni = mathceil((i + 1) / LOG_BASE);
  
              if (ni >= xc.length) {
  
                if (r) {
  
                  // Needed by sqrt.
                  for (; xc.length <= ni; xc.push(0));
                  n = rd = 0;
                  d = 1;
                  i %= LOG_BASE;
                  j = i - LOG_BASE + 1;
                } else {
                  break out;
                }
              } else {
                n = k = xc[ni];
  
                // Get the number of digits of n.
                for (d = 1; k >= 10; k /= 10, d++);
  
                // Get the index of rd within n.
                i %= LOG_BASE;
  
                // Get the index of rd within n, adjusted for leading zeros.
                // The number of leading zeros of n is given by LOG_BASE - d.
                j = i - LOG_BASE + d;
  
                // Get the rounding digit at index j of n.
                rd = j < 0 ? 0 : n / pows10[d - j - 1] % 10 | 0;
              }
            }
  
            r = r || sd < 0 ||
  
            // Are there any non-zero digits after the rounding digit?
            // The expression  n % pows10[d - j - 1]  returns all digits of n to the right
            // of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
             xc[ni + 1] != null || (j < 0 ? n : n % pows10[d - j - 1]);
  
            r = rm < 4
             ? (rd || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
             : rd > 5 || rd == 5 && (rm == 4 || r || rm == 6 &&
  
              // Check whether the digit to the left of the rounding digit is odd.
              ((i > 0 ? j > 0 ? n / pows10[d - j] : 0 : xc[ni - 1]) % 10) & 1 ||
               rm == (x.s < 0 ? 8 : 7));
  
            if (sd < 1 || !xc[0]) {
              xc.length = 0;
  
              if (r) {
  
                // Convert sd to decimal places.
                sd -= x.e + 1;
  
                // 1, 0.1, 0.01, 0.001, 0.0001 etc.
                xc[0] = pows10[(LOG_BASE - sd % LOG_BASE) % LOG_BASE];
                x.e = -sd || 0;
              } else {
  
                // Zero.
                xc[0] = x.e = 0;
              }
  
              return x;
            }
  
            // Remove excess digits.
            if (i == 0) {
              xc.length = ni;
              k = 1;
              ni--;
            } else {
              xc.length = ni + 1;
              k = pows10[LOG_BASE - i];
  
              // E.g. 56700 becomes 56000 if 7 is the rounding digit.
              // j > 0 means i > number of leading zeros of n.
              xc[ni] = j > 0 ? mathfloor(n / pows10[d - j] % pows10[j]) * k : 0;
            }
  
            // Round up?
            if (r) {
  
              for (; ;) {
  
                // If the digit to be rounded up is in the first element of xc...
                if (ni == 0) {
  
                  // i will be the length of xc[0] before k is added.
                  for (i = 1, j = xc[0]; j >= 10; j /= 10, i++);
                  j = xc[0] += k;
                  for (k = 1; j >= 10; j /= 10, k++);
  
                  // if i != k the length has increased.
                  if (i != k) {
                    x.e++;
                    if (xc[0] == BASE) xc[0] = 1;
                  }
  
                  break;
                } else {
                  xc[ni] += k;
                  if (xc[ni] != BASE) break;
                  xc[ni--] = 0;
                  k = 1;
                }
              }
            }
  
            // Remove trailing zeros.
            for (i = xc.length; xc[--i] === 0; xc.pop());
          }
  
          // Overflow? Infinity.
          if (x.e > MAX_EXP) {
            x.c = x.e = null;
  
          // Underflow? Zero.
          } else if (x.e < MIN_EXP) {
            x.c = [x.e = 0];
          }
        }
  
        return x;
      }
  
  
      function valueOf(n) {
        var str,
          e = n.e;
  
        if (e === null) return n.toString();
  
        str = coeffToString(n.c);
  
        str = e <= TO_EXP_NEG || e >= TO_EXP_POS
          ? toExponential(str, e)
          : toFixedPoint(str, e, '0');
  
        return n.s < 0 ? '-' + str : str;
      }
  
  
      // PROTOTYPE/INSTANCE METHODS
  
  
      /*
       * Return a new BigNumber whose value is the absolute value of this BigNumber.
       */
      P.absoluteValue = P.abs = function () {
        var x = new BigNumber(this);
        if (x.s < 0) x.s = 1;
        return x;
      };
  
  
      /*
       * Return
       *   1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
       *   -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
       *   0 if they have the same value,
       *   or null if the value of either is NaN.
       */
      P.comparedTo = function (y, b) {
        return compare(this, new BigNumber(y, b));
      };
  
  
      /*
       * If dp is undefined or null or true or false, return the number of decimal places of the
       * value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
       *
       * Otherwise, if dp is a number, return a new BigNumber whose value is the value of this
       * BigNumber rounded to a maximum of dp decimal places using rounding mode rm, or
       * ROUNDING_MODE if rm is omitted.
       *
       * [dp] {number} Decimal places: integer, 0 to MAX inclusive.
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       *
       * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
       */
      P.decimalPlaces = P.dp = function (dp, rm) {
        var c, n, v,
          x = this;
  
        if (dp != null) {
          intCheck(dp, 0, MAX);
          if (rm == null) rm = ROUNDING_MODE;
          else intCheck(rm, 0, 8);
  
          return round(new BigNumber(x), dp + x.e + 1, rm);
        }
  
        if (!(c = x.c)) return null;
        n = ((v = c.length - 1) - bitFloor(this.e / LOG_BASE)) * LOG_BASE;
  
        // Subtract the number of trailing zeros of the last number.
        if (v = c[v]) for (; v % 10 == 0; v /= 10, n--);
        if (n < 0) n = 0;
  
        return n;
      };
  
  
      /*
       *  n / 0 = I
       *  n / N = N
       *  n / I = 0
       *  0 / n = 0
       *  0 / 0 = N
       *  0 / N = N
       *  0 / I = 0
       *  N / n = N
       *  N / 0 = N
       *  N / N = N
       *  N / I = N
       *  I / n = I
       *  I / 0 = I
       *  I / N = N
       *  I / I = N
       *
       * Return a new BigNumber whose value is the value of this BigNumber divided by the value of
       * BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
       */
      P.dividedBy = P.div = function (y, b) {
        return div(this, new BigNumber(y, b), DECIMAL_PLACES, ROUNDING_MODE);
      };
  
  
      /*
       * Return a new BigNumber whose value is the integer part of dividing the value of this
       * BigNumber by the value of BigNumber(y, b).
       */
      P.dividedToIntegerBy = P.idiv = function (y, b) {
        return div(this, new BigNumber(y, b), 0, 1);
      };
  
  
      /*
       * Return a BigNumber whose value is the value of this BigNumber exponentiated by n.
       *
       * If m is present, return the result modulo m.
       * If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
       * If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using ROUNDING_MODE.
       *
       * The modular power operation works efficiently when x, n, and m are integers, otherwise it
       * is equivalent to calculating x.exponentiatedBy(n).modulo(m) with a POW_PRECISION of 0.
       *
       * n {number|string|BigNumber} The exponent. An integer.
       * [m] {number|string|BigNumber} The modulus.
       *
       * '[BigNumber Error] Exponent not an integer: {n}'
       */
      P.exponentiatedBy = P.pow = function (n, m) {
        var half, isModExp, i, k, more, nIsBig, nIsNeg, nIsOdd, y,
          x = this;
  
        n = new BigNumber(n);
  
        // Allow NaN and ±Infinity, but not other non-integers.
        if (n.c && !n.isInteger()) {
          throw Error
            (bignumberError + 'Exponent not an integer: ' + valueOf(n));
        }
  
        if (m != null) m = new BigNumber(m);
  
        // Exponent of MAX_SAFE_INTEGER is 15.
        nIsBig = n.e > 14;
  
        // If x is NaN, ±Infinity, ±0 or ±1, or n is ±Infinity, NaN or ±0.
        if (!x.c || !x.c[0] || x.c[0] == 1 && !x.e && x.c.length == 1 || !n.c || !n.c[0]) {
  
          // The sign of the result of pow when x is negative depends on the evenness of n.
          // If +n overflows to ±Infinity, the evenness of n would be not be known.
          y = new BigNumber(Math.pow(+valueOf(x), nIsBig ? 2 - isOdd(n) : +valueOf(n)));
          return m ? y.mod(m) : y;
        }
  
        nIsNeg = n.s < 0;
  
        if (m) {
  
          // x % m returns NaN if abs(m) is zero, or m is NaN.
          if (m.c ? !m.c[0] : !m.s) return new BigNumber(NaN);
  
          isModExp = !nIsNeg && x.isInteger() && m.isInteger();
  
          if (isModExp) x = x.mod(m);
  
        // Overflow to ±Infinity: >=2**1e10 or >=1.0000024**1e15.
        // Underflow to ±0: <=0.79**1e10 or <=0.9999975**1e15.
        } else if (n.e > 9 && (x.e > 0 || x.e < -1 || (x.e == 0
          // [1, 240000000]
          ? x.c[0] > 1 || nIsBig && x.c[1] >= 24e7
          // [80000000000000]  [99999750000000]
          : x.c[0] < 8e13 || nIsBig && x.c[0] <= 9999975e7))) {
  
          // If x is negative and n is odd, k = -0, else k = 0.
          k = x.s < 0 && isOdd(n) ? -0 : 0;
  
          // If x >= 1, k = ±Infinity.
          if (x.e > -1) k = 1 / k;
  
          // If n is negative return ±0, else return ±Infinity.
          return new BigNumber(nIsNeg ? 1 / k : k);
  
        } else if (POW_PRECISION) {
  
          // Truncating each coefficient array to a length of k after each multiplication
          // equates to truncating significant digits to POW_PRECISION + [28, 41],
          // i.e. there will be a minimum of 28 guard digits retained.
          k = mathceil(POW_PRECISION / LOG_BASE + 2);
        }
  
        if (nIsBig) {
          half = new BigNumber(0.5);
          if (nIsNeg) n.s = 1;
          nIsOdd = isOdd(n);
        } else {
          i = Math.abs(+valueOf(n));
          nIsOdd = i % 2;
        }
  
        y = new BigNumber(ONE);
  
        // Performs 54 loop iterations for n of 9007199254740991.
        for (; ;) {
  
          if (nIsOdd) {
            y = y.times(x);
            if (!y.c) break;
  
            if (k) {
              if (y.c.length > k) y.c.length = k;
            } else if (isModExp) {
              y = y.mod(m);    //y = y.minus(div(y, m, 0, MODULO_MODE).times(m));
            }
          }
  
          if (i) {
            i = mathfloor(i / 2);
            if (i === 0) break;
            nIsOdd = i % 2;
          } else {
            n = n.times(half);
            round(n, n.e + 1, 1);
  
            if (n.e > 14) {
              nIsOdd = isOdd(n);
            } else {
              i = +valueOf(n);
              if (i === 0) break;
              nIsOdd = i % 2;
            }
          }
  
          x = x.times(x);
  
          if (k) {
            if (x.c && x.c.length > k) x.c.length = k;
          } else if (isModExp) {
            x = x.mod(m);    //x = x.minus(div(x, m, 0, MODULO_MODE).times(m));
          }
        }
  
        if (isModExp) return y;
        if (nIsNeg) y = ONE.div(y);
  
        return m ? y.mod(m) : k ? round(y, POW_PRECISION, ROUNDING_MODE, more) : y;
      };
  
  
      /*
       * Return a new BigNumber whose value is the value of this BigNumber rounded to an integer
       * using rounding mode rm, or ROUNDING_MODE if rm is omitted.
       *
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       *
       * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {rm}'
       */
      P.integerValue = function (rm) {
        var n = new BigNumber(this);
        if (rm == null) rm = ROUNDING_MODE;
        else intCheck(rm, 0, 8);
        return round(n, n.e + 1, rm);
      };
  
  
      /*
       * Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
       * otherwise return false.
       */
      P.isEqualTo = P.eq = function (y, b) {
        return compare(this, new BigNumber(y, b)) === 0;
      };
  
  
      /*
       * Return true if the value of this BigNumber is a finite number, otherwise return false.
       */
      P.isFinite = function () {
        return !!this.c;
      };
  
  
      /*
       * Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
       * otherwise return false.
       */
      P.isGreaterThan = P.gt = function (y, b) {
        return compare(this, new BigNumber(y, b)) > 0;
      };
  
  
      /*
       * Return true if the value of this BigNumber is greater than or equal to the value of
       * BigNumber(y, b), otherwise return false.
       */
      P.isGreaterThanOrEqualTo = P.gte = function (y, b) {
        return (b = compare(this, new BigNumber(y, b))) === 1 || b === 0;
  
      };
  
  
      /*
       * Return true if the value of this BigNumber is an integer, otherwise return false.
       */
      P.isInteger = function () {
        return !!this.c && bitFloor(this.e / LOG_BASE) > this.c.length - 2;
      };
  
  
      /*
       * Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
       * otherwise return false.
       */
      P.isLessThan = P.lt = function (y, b) {
        return compare(this, new BigNumber(y, b)) < 0;
      };
  
  
      /*
       * Return true if the value of this BigNumber is less than or equal to the value of
       * BigNumber(y, b), otherwise return false.
       */
      P.isLessThanOrEqualTo = P.lte = function (y, b) {
        return (b = compare(this, new BigNumber(y, b))) === -1 || b === 0;
      };
  
  
      /*
       * Return true if the value of this BigNumber is NaN, otherwise return false.
       */
      P.isNaN = function () {
        return !this.s;
      };
  
  
      /*
       * Return true if the value of this BigNumber is negative, otherwise return false.
       */
      P.isNegative = function () {
        return this.s < 0;
      };
  
  
      /*
       * Return true if the value of this BigNumber is positive, otherwise return false.
       */
      P.isPositive = function () {
        return this.s > 0;
      };
  
  
      /*
       * Return true if the value of this BigNumber is 0 or -0, otherwise return false.
       */
      P.isZero = function () {
        return !!this.c && this.c[0] == 0;
      };
  
  
      /*
       *  n - 0 = n
       *  n - N = N
       *  n - I = -I
       *  0 - n = -n
       *  0 - 0 = 0
       *  0 - N = N
       *  0 - I = -I
       *  N - n = N
       *  N - 0 = N
       *  N - N = N
       *  N - I = N
       *  I - n = I
       *  I - 0 = I
       *  I - N = N
       *  I - I = N
       *
       * Return a new BigNumber whose value is the value of this BigNumber minus the value of
       * BigNumber(y, b).
       */
      P.minus = function (y, b) {
        var i, j, t, xLTy,
          x = this,
          a = x.s;
  
        y = new BigNumber(y, b);
        b = y.s;
  
        // Either NaN?
        if (!a || !b) return new BigNumber(NaN);
  
        // Signs differ?
        if (a != b) {
          y.s = -b;
          return x.plus(y);
        }
  
        var xe = x.e / LOG_BASE,
          ye = y.e / LOG_BASE,
          xc = x.c,
          yc = y.c;
  
        if (!xe || !ye) {
  
          // Either Infinity?
          if (!xc || !yc) return xc ? (y.s = -b, y) : new BigNumber(yc ? x : NaN);
  
          // Either zero?
          if (!xc[0] || !yc[0]) {
  
            // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
            return yc[0] ? (y.s = -b, y) : new BigNumber(xc[0] ? x :
  
             // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
             ROUNDING_MODE == 3 ? -0 : 0);
          }
        }
  
        xe = bitFloor(xe);
        ye = bitFloor(ye);
        xc = xc.slice();
  
        // Determine which is the bigger number.
        if (a = xe - ye) {
  
          if (xLTy = a < 0) {
            a = -a;
            t = xc;
          } else {
            ye = xe;
            t = yc;
          }
  
          t.reverse();
  
          // Prepend zeros to equalise exponents.
          for (b = a; b--; t.push(0));
          t.reverse();
        } else {
  
          // Exponents equal. Check digit by digit.
          j = (xLTy = (a = xc.length) < (b = yc.length)) ? a : b;
  
          for (a = b = 0; b < j; b++) {
  
            if (xc[b] != yc[b]) {
              xLTy = xc[b] < yc[b];
              break;
            }
          }
        }
  
        // x < y? Point xc to the array of the bigger number.
        if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
  
        b = (j = yc.length) - (i = xc.length);
  
        // Append zeros to xc if shorter.
        // No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
        if (b > 0) for (; b--; xc[i++] = 0);
        b = BASE - 1;
  
        // Subtract yc from xc.
        for (; j > a;) {
  
          if (xc[--j] < yc[j]) {
            for (i = j; i && !xc[--i]; xc[i] = b);
            --xc[i];
            xc[j] += BASE;
          }
  
          xc[j] -= yc[j];
        }
  
        // Remove leading zeros and adjust exponent accordingly.
        for (; xc[0] == 0; xc.splice(0, 1), --ye);
  
        // Zero?
        if (!xc[0]) {
  
          // Following IEEE 754 (2008) 6.3,
          // n - n = +0  but  n - n = -0  when rounding towards -Infinity.
          y.s = ROUNDING_MODE == 3 ? -1 : 1;
          y.c = [y.e = 0];
          return y;
        }
  
        // No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
        // for finite x and y.
        return normalise(y, xc, ye);
      };
  
  
      /*
       *   n % 0 =  N
       *   n % N =  N
       *   n % I =  n
       *   0 % n =  0
       *  -0 % n = -0
       *   0 % 0 =  N
       *   0 % N =  N
       *   0 % I =  0
       *   N % n =  N
       *   N % 0 =  N
       *   N % N =  N
       *   N % I =  N
       *   I % n =  N
       *   I % 0 =  N
       *   I % N =  N
       *   I % I =  N
       *
       * Return a new BigNumber whose value is the value of this BigNumber modulo the value of
       * BigNumber(y, b). The result depends on the value of MODULO_MODE.
       */
      P.modulo = P.mod = function (y, b) {
        var q, s,
          x = this;
  
        y = new BigNumber(y, b);
  
        // Return NaN if x is Infinity or NaN, or y is NaN or zero.
        if (!x.c || !y.s || y.c && !y.c[0]) {
          return new BigNumber(NaN);
  
        // Return x if y is Infinity or x is zero.
        } else if (!y.c || x.c && !x.c[0]) {
          return new BigNumber(x);
        }
  
        if (MODULO_MODE == 9) {
  
          // Euclidian division: q = sign(y) * floor(x / abs(y))
          // r = x - qy    where  0 <= r < abs(y)
          s = y.s;
          y.s = 1;
          q = div(x, y, 0, 3);
          y.s = s;
          q.s *= s;
        } else {
          q = div(x, y, 0, MODULO_MODE);
        }
  
        y = x.minus(q.times(y));
  
        // To match JavaScript %, ensure sign of zero is sign of dividend.
        if (!y.c[0] && MODULO_MODE == 1) y.s = x.s;
  
        return y;
      };
  
  
      /*
       *  n * 0 = 0
       *  n * N = N
       *  n * I = I
       *  0 * n = 0
       *  0 * 0 = 0
       *  0 * N = N
       *  0 * I = N
       *  N * n = N
       *  N * 0 = N
       *  N * N = N
       *  N * I = N
       *  I * n = I
       *  I * 0 = N
       *  I * N = N
       *  I * I = I
       *
       * Return a new BigNumber whose value is the value of this BigNumber multiplied by the value
       * of BigNumber(y, b).
       */
      P.multipliedBy = P.times = function (y, b) {
        var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
          base, sqrtBase,
          x = this,
          xc = x.c,
          yc = (y = new BigNumber(y, b)).c;
  
        // Either NaN, ±Infinity or ±0?
        if (!xc || !yc || !xc[0] || !yc[0]) {
  
          // Return NaN if either is NaN, or one is 0 and the other is Infinity.
          if (!x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc) {
            y.c = y.e = y.s = null;
          } else {
            y.s *= x.s;
  
            // Return ±Infinity if either is ±Infinity.
            if (!xc || !yc) {
              y.c = y.e = null;
  
            // Return ±0 if either is ±0.
            } else {
              y.c = [0];
              y.e = 0;
            }
          }
  
          return y;
        }
  
        e = bitFloor(x.e / LOG_BASE) + bitFloor(y.e / LOG_BASE);
        y.s *= x.s;
        xcL = xc.length;
        ycL = yc.length;
  
        // Ensure xc points to longer array and xcL to its length.
        if (xcL < ycL) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
  
        // Initialise the result array with zeros.
        for (i = xcL + ycL, zc = []; i--; zc.push(0));
  
        base = BASE;
        sqrtBase = SQRT_BASE;
  
        for (i = ycL; --i >= 0;) {
          c = 0;
          ylo = yc[i] % sqrtBase;
          yhi = yc[i] / sqrtBase | 0;
  
          for (k = xcL, j = i + k; j > i;) {
            xlo = xc[--k] % sqrtBase;
            xhi = xc[k] / sqrtBase | 0;
            m = yhi * xlo + xhi * ylo;
            xlo = ylo * xlo + ((m % sqrtBase) * sqrtBase) + zc[j] + c;
            c = (xlo / base | 0) + (m / sqrtBase | 0) + yhi * xhi;
            zc[j--] = xlo % base;
          }
  
          zc[j] = c;
        }
  
        if (c) {
          ++e;
        } else {
          zc.splice(0, 1);
        }
  
        return normalise(y, zc, e);
      };
  
  
      /*
       * Return a new BigNumber whose value is the value of this BigNumber negated,
       * i.e. multiplied by -1.
       */
      P.negated = function () {
        var x = new BigNumber(this);
        x.s = -x.s || null;
        return x;
      };
  
  
      /*
       *  n + 0 = n
       *  n + N = N
       *  n + I = I
       *  0 + n = n
       *  0 + 0 = 0
       *  0 + N = N
       *  0 + I = I
       *  N + n = N
       *  N + 0 = N
       *  N + N = N
       *  N + I = N
       *  I + n = I
       *  I + 0 = I
       *  I + N = N
       *  I + I = I
       *
       * Return a new BigNumber whose value is the value of this BigNumber plus the value of
       * BigNumber(y, b).
       */
      P.plus = function (y, b) {
        var t,
          x = this,
          a = x.s;
  
        y = new BigNumber(y, b);
        b = y.s;
  
        // Either NaN?
        if (!a || !b) return new BigNumber(NaN);
  
        // Signs differ?
         if (a != b) {
          y.s = -b;
          return x.minus(y);
        }
  
        var xe = x.e / LOG_BASE,
          ye = y.e / LOG_BASE,
          xc = x.c,
          yc = y.c;
  
        if (!xe || !ye) {
  
          // Return ±Infinity if either ±Infinity.
          if (!xc || !yc) return new BigNumber(a / 0);
  
          // Either zero?
          // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
          if (!xc[0] || !yc[0]) return yc[0] ? y : new BigNumber(xc[0] ? x : a * 0);
        }
  
        xe = bitFloor(xe);
        ye = bitFloor(ye);
        xc = xc.slice();
  
        // Prepend zeros to equalise exponents. Faster to use reverse then do unshifts.
        if (a = xe - ye) {
          if (a > 0) {
            ye = xe;
            t = yc;
          } else {
            a = -a;
            t = xc;
          }
  
          t.reverse();
          for (; a--; t.push(0));
          t.reverse();
        }
  
        a = xc.length;
        b = yc.length;
  
        // Point xc to the longer array, and b to the shorter length.
        if (a - b < 0) t = yc, yc = xc, xc = t, b = a;
  
        // Only start adding at yc.length - 1 as the further digits of xc can be ignored.
        for (a = 0; b;) {
          a = (xc[--b] = xc[b] + yc[b] + a) / BASE | 0;
          xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
        }
  
        if (a) {
          xc = [a].concat(xc);
          ++ye;
        }
  
        // No need to check for zero, as +x + +y != 0 && -x + -y != 0
        // ye = MAX_EXP + 1 possible
        return normalise(y, xc, ye);
      };
  
  
      /*
       * If sd is undefined or null or true or false, return the number of significant digits of
       * the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
       * If sd is true include integer-part trailing zeros in the count.
       *
       * Otherwise, if sd is a number, return a new BigNumber whose value is the value of this
       * BigNumber rounded to a maximum of sd significant digits using rounding mode rm, or
       * ROUNDING_MODE if rm is omitted.
       *
       * sd {number|boolean} number: significant digits: integer, 1 to MAX inclusive.
       *                     boolean: whether to count integer-part trailing zeros: true or false.
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       *
       * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
       */
      P.precision = P.sd = function (sd, rm) {
        var c, n, v,
          x = this;
  
        if (sd != null && sd !== !!sd) {
          intCheck(sd, 1, MAX);
          if (rm == null) rm = ROUNDING_MODE;
          else intCheck(rm, 0, 8);
  
          return round(new BigNumber(x), sd, rm);
        }
  
        if (!(c = x.c)) return null;
        v = c.length - 1;
        n = v * LOG_BASE + 1;
  
        if (v = c[v]) {
  
          // Subtract the number of trailing zeros of the last element.
          for (; v % 10 == 0; v /= 10, n--);
  
          // Add the number of digits of the first element.
          for (v = c[0]; v >= 10; v /= 10, n++);
        }
  
        if (sd && x.e + 1 > n) n = x.e + 1;
  
        return n;
      };
  
  
      /*
       * Return a new BigNumber whose value is the value of this BigNumber shifted by k places
       * (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
       *
       * k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
       *
       * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {k}'
       */
      P.shiftedBy = function (k) {
        intCheck(k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER);
        return this.times('1e' + k);
      };
  
  
      /*
       *  sqrt(-n) =  N
       *  sqrt(N) =  N
       *  sqrt(-I) =  N
       *  sqrt(I) =  I
       *  sqrt(0) =  0
       *  sqrt(-0) = -0
       *
       * Return a new BigNumber whose value is the square root of the value of this BigNumber,
       * rounded according to DECIMAL_PLACES and ROUNDING_MODE.
       */
      P.squareRoot = P.sqrt = function () {
        var m, n, r, rep, t,
          x = this,
          c = x.c,
          s = x.s,
          e = x.e,
          dp = DECIMAL_PLACES + 4,
          half = new BigNumber('0.5');
  
        // Negative/NaN/Infinity/zero?
        if (s !== 1 || !c || !c[0]) {
          return new BigNumber(!s || s < 0 && (!c || c[0]) ? NaN : c ? x : 1 / 0);
        }
  
        // Initial estimate.
        s = Math.sqrt(+valueOf(x));
  
        // Math.sqrt underflow/overflow?
        // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
        if (s == 0 || s == 1 / 0) {
          n = coeffToString(c);
          if ((n.length + e) % 2 == 0) n += '0';
          s = Math.sqrt(+n);
          e = bitFloor((e + 1) / 2) - (e < 0 || e % 2);
  
          if (s == 1 / 0) {
            n = '5e' + e;
          } else {
            n = s.toExponential();
            n = n.slice(0, n.indexOf('e') + 1) + e;
          }
  
          r = new BigNumber(n);
        } else {
          r = new BigNumber(s + '');
        }
  
        // Check for zero.
        // r could be zero if MIN_EXP is changed after the this value was created.
        // This would cause a division by zero (x/t) and hence Infinity below, which would cause
        // coeffToString to throw.
        if (r.c[0]) {
          e = r.e;
          s = e + dp;
          if (s < 3) s = 0;
  
          // Newton-Raphson iteration.
          for (; ;) {
            t = r;
            r = half.times(t.plus(div(x, t, dp, 1)));
  
            if (coeffToString(t.c).slice(0, s) === (n = coeffToString(r.c)).slice(0, s)) {
  
              // The exponent of r may here be one less than the final result exponent,
              // e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
              // are indexed correctly.
              if (r.e < e) --s;
              n = n.slice(s - 3, s + 1);
  
              // The 4th rounding digit may be in error by -1 so if the 4 rounding digits
              // are 9999 or 4999 (i.e. approaching a rounding boundary) continue the
              // iteration.
              if (n == '9999' || !rep && n == '4999') {
  
                // On the first iteration only, check to see if rounding up gives the
                // exact result as the nines may infinitely repeat.
                if (!rep) {
                  round(t, t.e + DECIMAL_PLACES + 2, 0);
  
                  if (t.times(t).eq(x)) {
                    r = t;
                    break;
                  }
                }
  
                dp += 4;
                s += 4;
                rep = 1;
              } else {
  
                // If rounding digits are null, 0{0,4} or 50{0,3}, check for exact
                // result. If not, then there are further digits and m will be truthy.
                if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
  
                  // Truncate to the first rounding digit.
                  round(r, r.e + DECIMAL_PLACES + 2, 1);
                  m = !r.times(r).eq(x);
                }
  
                break;
              }
            }
          }
        }
  
        return round(r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m);
      };
  
  
      /*
       * Return a string representing the value of this BigNumber in exponential notation and
       * rounded using ROUNDING_MODE to dp fixed decimal places.
       *
       * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       *
       * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
       */
      P.toExponential = function (dp, rm) {
        if (dp != null) {
          intCheck(dp, 0, MAX);
          dp++;
        }
        return format(this, dp, rm, 1);
      };
  
  
      /*
       * Return a string representing the value of this BigNumber in fixed-point notation rounding
       * to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
       *
       * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
       * but e.g. (-0.00001).toFixed(0) is '-0'.
       *
       * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       *
       * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
       */
      P.toFixed = function (dp, rm) {
        if (dp != null) {
          intCheck(dp, 0, MAX);
          dp = dp + this.e + 1;
        }
        return format(this, dp, rm);
      };
  
  
      /*
       * Return a string representing the value of this BigNumber in fixed-point notation rounded
       * using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
       * of the format or FORMAT object (see BigNumber.set).
       *
       * The formatting object may contain some or all of the properties shown below.
       *
       * FORMAT = {
       *   prefix: '',
       *   groupSize: 3,
       *   secondaryGroupSize: 0,
       *   groupSeparator: ',',
       *   decimalSeparator: '.',
       *   fractionGroupSize: 0,
       *   fractionGroupSeparator: '\xA0',      // non-breaking space
       *   suffix: ''
       * };
       *
       * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       * [format] {object} Formatting options. See FORMAT pbject above.
       *
       * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
       * '[BigNumber Error] Argument not an object: {format}'
       */
      P.toFormat = function (dp, rm, format) {
        var str,
          x = this;
  
        if (format == null) {
          if (dp != null && rm && typeof rm == 'object') {
            format = rm;
            rm = null;
          } else if (dp && typeof dp == 'object') {
            format = dp;
            dp = rm = null;
          } else {
            format = FORMAT;
          }
        } else if (typeof format != 'object') {
          throw Error
            (bignumberError + 'Argument not an object: ' + format);
        }
  
        str = x.toFixed(dp, rm);
  
        if (x.c) {
          var i,
            arr = str.split('.'),
            g1 = +format.groupSize,
            g2 = +format.secondaryGroupSize,
            groupSeparator = format.groupSeparator || '',
            intPart = arr[0],
            fractionPart = arr[1],
            isNeg = x.s < 0,
            intDigits = isNeg ? intPart.slice(1) : intPart,
            len = intDigits.length;
  
          if (g2) i = g1, g1 = g2, g2 = i, len -= i;
  
          if (g1 > 0 && len > 0) {
            i = len % g1 || g1;
            intPart = intDigits.substr(0, i);
            for (; i < len; i += g1) intPart += groupSeparator + intDigits.substr(i, g1);
            if (g2 > 0) intPart += groupSeparator + intDigits.slice(i);
            if (isNeg) intPart = '-' + intPart;
          }
  
          str = fractionPart
           ? intPart + (format.decimalSeparator || '') + ((g2 = +format.fractionGroupSize)
            ? fractionPart.replace(new RegExp('\\d{' + g2 + '}\\B', 'g'),
             '$&' + (format.fractionGroupSeparator || ''))
            : fractionPart)
           : intPart;
        }
  
        return (format.prefix || '') + str + (format.suffix || '');
      };
  
  
      /*
       * Return an array of two BigNumbers representing the value of this BigNumber as a simple
       * fraction with an integer numerator and an integer denominator.
       * The denominator will be a positive non-zero value less than or equal to the specified
       * maximum denominator. If a maximum denominator is not specified, the denominator will be
       * the lowest value necessary to represent the number exactly.
       *
       * [md] {number|string|BigNumber} Integer >= 1, or Infinity. The maximum denominator.
       *
       * '[BigNumber Error] Argument {not an integer|out of range} : {md}'
       */
      P.toFraction = function (md) {
        var d, d0, d1, d2, e, exp, n, n0, n1, q, r, s,
          x = this,
          xc = x.c;
  
        if (md != null) {
          n = new BigNumber(md);
  
          // Throw if md is less than one or is not an integer, unless it is Infinity.
          if (!n.isInteger() && (n.c || n.s !== 1) || n.lt(ONE)) {
            throw Error
              (bignumberError + 'Argument ' +
                (n.isInteger() ? 'out of range: ' : 'not an integer: ') + valueOf(n));
          }
        }
  
        if (!xc) return new BigNumber(x);
  
        d = new BigNumber(ONE);
        n1 = d0 = new BigNumber(ONE);
        d1 = n0 = new BigNumber(ONE);
        s = coeffToString(xc);
  
        // Determine initial denominator.
        // d is a power of 10 and the minimum max denominator that specifies the value exactly.
        e = d.e = s.length - x.e - 1;
        d.c[0] = POWS_TEN[(exp = e % LOG_BASE) < 0 ? LOG_BASE + exp : exp];
        md = !md || n.comparedTo(d) > 0 ? (e > 0 ? d : n1) : n;
  
        exp = MAX_EXP;
        MAX_EXP = 1 / 0;
        n = new BigNumber(s);
  
        // n0 = d1 = 0
        n0.c[0] = 0;
  
        for (; ;)  {
          q = div(n, d, 0, 1);
          d2 = d0.plus(q.times(d1));
          if (d2.comparedTo(md) == 1) break;
          d0 = d1;
          d1 = d2;
          n1 = n0.plus(q.times(d2 = n1));
          n0 = d2;
          d = n.minus(q.times(d2 = d));
          n = d2;
        }
  
        d2 = div(md.minus(d0), d1, 0, 1);
        n0 = n0.plus(d2.times(n1));
        d0 = d0.plus(d2.times(d1));
        n0.s = n1.s = x.s;
        e = e * 2;
  
        // Determine which fraction is closer to x, n0/d0 or n1/d1
        r = div(n1, d1, e, ROUNDING_MODE).minus(x).abs().comparedTo(
            div(n0, d0, e, ROUNDING_MODE).minus(x).abs()) < 1 ? [n1, d1] : [n0, d0];
  
        MAX_EXP = exp;
  
        return r;
      };
  
  
      /*
       * Return the value of this BigNumber converted to a number primitive.
       */
      P.toNumber = function () {
        return +valueOf(this);
      };
  
  
      /*
       * Return a string representing the value of this BigNumber rounded to sd significant digits
       * using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
       * necessary to represent the integer part of the value in fixed-point notation, then use
       * exponential notation.
       *
       * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       *
       * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
       */
      P.toPrecision = function (sd, rm) {
        if (sd != null) intCheck(sd, 1, MAX);
        return format(this, sd, rm, 2);
      };
  
  
      /*
       * Return a string representing the value of this BigNumber in base b, or base 10 if b is
       * omitted. If a base is specified, including base 10, round according to DECIMAL_PLACES and
       * ROUNDING_MODE. If a base is not specified, and this BigNumber has a positive exponent
       * that is equal to or greater than TO_EXP_POS, or a negative exponent equal to or less than
       * TO_EXP_NEG, return exponential notation.
       *
       * [b] {number} Integer, 2 to ALPHABET.length inclusive.
       *
       * '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
       */
      P.toString = function (b) {
        var str,
          n = this,
          s = n.s,
          e = n.e;
  
        // Infinity or NaN?
        if (e === null) {
          if (s) {
            str = 'Infinity';
            if (s < 0) str = '-' + str;
          } else {
            str = 'NaN';
          }
        } else {
          if (b == null) {
            str = e <= TO_EXP_NEG || e >= TO_EXP_POS
             ? toExponential(coeffToString(n.c), e)
             : toFixedPoint(coeffToString(n.c), e, '0');
          } else if (b === 10) {
            n = round(new BigNumber(n), DECIMAL_PLACES + e + 1, ROUNDING_MODE);
            str = toFixedPoint(coeffToString(n.c), n.e, '0');
          } else {
            intCheck(b, 2, ALPHABET.length, 'Base');
            str = convertBase(toFixedPoint(coeffToString(n.c), e, '0'), 10, b, s, true);
          }
  
          if (s < 0 && n.c[0]) str = '-' + str;
        }
  
        return str;
      };
  
  
      /*
       * Return as toString, but do not accept a base argument, and include the minus sign for
       * negative zero.
       */
      P.valueOf = P.toJSON = function () {
        return valueOf(this);
      };
  
  
      P._isBigNumber = true;
  
      if (configObject != null) BigNumber.set(configObject);
  
      return BigNumber;
    }
  
  
    // PRIVATE HELPER FUNCTIONS
  
    // These functions don't need access to variables,
    // e.g. DECIMAL_PLACES, in the scope of the `clone` function above.
  
  
    function bitFloor(n) {
      var i = n | 0;
      return n > 0 || n === i ? i : i - 1;
    }
  
  
    // Return a coefficient array as a string of base 10 digits.
    function coeffToString(a) {
      var s, z,
        i = 1,
        j = a.length,
        r = a[0] + '';
  
      for (; i < j;) {
        s = a[i++] + '';
        z = LOG_BASE - s.length;
        for (; z--; s = '0' + s);
        r += s;
      }
  
      // Determine trailing zeros.
      for (j = r.length; r.charCodeAt(--j) === 48;);
  
      return r.slice(0, j + 1 || 1);
    }
  
  
    // Compare the value of BigNumbers x and y.
    function compare(x, y) {
      var a, b,
        xc = x.c,
        yc = y.c,
        i = x.s,
        j = y.s,
        k = x.e,
        l = y.e;
  
      // Either NaN?
      if (!i || !j) return null;
  
      a = xc && !xc[0];
      b = yc && !yc[0];
  
      // Either zero?
      if (a || b) return a ? b ? 0 : -j : i;
  
      // Signs differ?
      if (i != j) return i;
  
      a = i < 0;
      b = k == l;
  
      // Either Infinity?
      if (!xc || !yc) return b ? 0 : !xc ^ a ? 1 : -1;
  
      // Compare exponents.
      if (!b) return k > l ^ a ? 1 : -1;
  
      j = (k = xc.length) < (l = yc.length) ? k : l;
  
      // Compare digit by digit.
      for (i = 0; i < j; i++) if (xc[i] != yc[i]) return xc[i] > yc[i] ^ a ? 1 : -1;
  
      // Compare lengths.
      return k == l ? 0 : k > l ^ a ? 1 : -1;
    }
  
  
    /*
     * Check that n is a primitive number, an integer, and in range, otherwise throw.
     */
    function intCheck(n, min, max, name) {
      if (n < min || n > max || n !== mathfloor(n)) {
        throw Error
         (bignumberError + (name || 'Argument') + (typeof n == 'number'
           ? n < min || n > max ? ' out of range: ' : ' not an integer: '
           : ' not a primitive number: ') + String(n));
      }
    }
  
  
    // Assumes finite n.
    function isOdd(n) {
      var k = n.c.length - 1;
      return bitFloor(n.e / LOG_BASE) == k && n.c[k] % 2 != 0;
    }
  
  
    function toExponential(str, e) {
      return (str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str) +
       (e < 0 ? 'e' : 'e+') + e;
    }
  
  
    function toFixedPoint(str, e, z) {
      var len, zs;
  
      // Negative exponent?
      if (e < 0) {
  
        // Prepend zeros.
        for (zs = z + '.'; ++e; zs += z);
        str = zs + str;
  
      // Positive exponent
      } else {
        len = str.length;
  
        // Append zeros.
        if (++e > len) {
          for (zs = z, e -= len; --e; zs += z);
          str += zs;
        } else if (e < len) {
          str = str.slice(0, e) + '.' + str.slice(e);
        }
      }
  
      return str;
    }
  
  
    // EXPORT
  
  
    BigNumber = clone();
    BigNumber['default'] = BigNumber.BigNumber = BigNumber;
  
    // AMD.
    if (typeof define == 'function' && define.amd) {
      define(function () { return BigNumber; });
  
    // Node.js and other environments that support module.exports.
    } else if (typeof module != 'undefined' && module.exports) {
      module.exports = BigNumber;
  
    // Browser.
    } else {
      if (!globalObject) {
        globalObject = typeof self != 'undefined' && self ? self : window;
      }
  
      globalObject.BigNumber = BigNumber;
    }
  })(this);